Heave Plates Research Articles

Numerical study of hydrodynamic coefficients of multiple heave plates by large eddy simulations with volume of fluid method

Hydrodynamic coefficients of multiple heave plates are studied for offshore structures to reduce heave responses in oscillating flows. Large eddy simulations with volume of fluid method are performed to predict the hydrodynamic force on a forced oscillated model with multiple heave plates. Predicted added mass and drag coefficients are validated by a water tank test. Then, flow pattern around the multiple heave plates is investigated to clarify the mechanism of hydrodynamic forces on each plate, and a systematic study on the effects of geometric parameters, such as spacing ratio, diameter ratio and aspect ratio on the hydrodynamics of octagonal heave plate are conducted. Finally, formulas of added mass and drag coefficients for a single and double heave plates with circular, octagonal and square cross-sections are proposed to cover a wide range of application of the heave plate.

SPH Simulation of Wave Scattering by a Heaving Submerged Horizontal Plate

Liu et al. [Liu, C., Huang, Z. & Chen, W. [2017] “A numerical study of a submerged horizontal heaving plate as a breakwater,” J. Coast. Res.33(4), 917–930.] numerically studied the wave scattering by a heaving submerged horizontal plate (SHP) within the framework of the potential flow theory. They presented the excellent performance of the heaving SHP on wave blocking, because the radiated wave induced by the heave response of plate is likely to neutralize the transmitted wave. As a further study, the present work simulates the wave–heaving SHP interaction using the smoothed particle hydrodynamics, which is widely recognized as a powerful tool for computing complex viscous fluid dynamics. In this way, additional understanding on the wave blocking mechanism of the heaving SHP is contributed. The effect of submergence of plate on the wave and structural dynamics is also investigated. The results show that, under most submergence conditions, a heaving SHP breakwater is more effective than a fixed one. In terms of the limited cases in this research, 17% is proven to be the optimum ratio of submergence to water depth for the heaving SHP breakwater.

Experimental and numerical investigation of a taut-moored wave energy converter: A validation of simulated buoy motions

This study presents an experimental and numerical investigation of a taut-moored wave energy converter (WEC) system with a point absorber type of WEC. The WEC system consists of a buoy, a unique three-leg two-segment mooring system with submerged floaters, and a power take-off system designed for the current experiment as a heave plate. The main objective of the study is to validate a numerical simulation model against experiments carried out in an ocean basin laboratory. Two physical models in model scales 1:20 and 1:36 were built and tested. The detailed experimental testing program encompasses tests of mooring system stiffness, decay tests, and different sea state conditions for ocean current, regular and irregular waves. A numerical model in the model scale 1:20 was developed to simulate coupled hydrodynamic and structural response analyses of the WEC system, primarily using potential flow theory, boundary element method, finite element method, and the Morison equation. Several numerical simulations are presented for each part of the experimental testing program. Results for the WEC buoy motions under operational conditions from the experiments and the numerical simulations were compared. This study shows that the simulation model can satisfactorily predict the dynamic motion responses of the WEC system at non-resonant conditions while at resonant conditions additional calibration is needed to capture the damping present during the experiment. A discussion on simulation model calibration with regard to linear and non-linear damping highlights the challenge to estimate these damping values if measurement data are not available.

A mechanism of thrust enhancement on a heaving plate due to flexibility at moderately low Reynolds numbers

A numerical study is conducted to investigate the force mechanisms for a 3D heaving flexible plate from the perspective of a diagnostic force element analysis. The problem is relevant to a flapping fish-tail simplified as a flat plate with the leading edge held heaving in the space. The flow is assumed to be laminar with the Reynolds numbers fixed at Re=200 or 500, and the Strouhal number St ranging from 0.1 to 0.6, and the flexure amplitude of the plate a0 from 0.1 to 0.25 (dimensionless). As the finite plate is set into unsteady motion, complicated vortex patterns around the plate are generated. It is shown that heaving, whilst increasing thrust generation, also reduces the frictional drag, yet the flexibility promotes thrust generation at the expense of accruing more frictional drag. In the literature, the force (thrust) exerted on the tail-mimicking plate is largely credited to the vortices (vorticity) in the wake. However, this study performs a regional force analysis to show that the vorticity in the wake region supplies approximately 20–30% of the total thrust, especially in the cases of strong thrust generation. Comparable contributions come also from the regions direct above and below the heaving plate (mainly including the attached vortices) as well as from the two side regions (mainly including the tip vortices) next to the flexible plate. In addition, the potential motion associated with the unsteady flapping and the contribution from the surface vorticity are non-negligible constituent force components. The relative importance of the various force contributions was analyzed in detail, and the results may shed light on how a flapping tail generates propulsive efficiency above the critical Strouhal number St=0.2.

Investigation of heave response of the deepwater octagonal FDPSO using various heave plate configurations

Heave plates can be employed to control undesirable heave motion amplitudes of the deepwater octagonal Floating, Drilling, Production, Storage, and Offloading (FDPSO) platform. Numerical simulations and model tests were applied to analyze and investigate the hydrodynamic response and the feasibility of the heave plate configurations. The diameter and the depth below the free surface of a single-layer heave plate, as well as the spacing of two-layer heave plates, were considered as the primary variables when studying the effect of heave plates on FDPSO hydrodynamics. The analysis results indicate that the heave plate diameter significantly affects the heave hydrodynamics, and heave performance could be improved with an increased diameter. In addition, increasing the depth below the free surface of a single-layer heave plate does not effectively suppress the heave motion within the range of draft depths tested. The target FDPSO obtained better heave characteristics with increased spacing between the two-layer heave plates. Furthermore, the global performances of the octagonal FDPSO with these typical heave plate configurations were comparatively analyzed. The results indicate that from a hydrodynamic point of view, the single-layer heave plate configuration has an advantage over the two-layer heave plate configuration.

Motions of a 5 MW floating VAWT evaluated by numerical simulations and model tests

The VAWT (vertical axis wind turbine) has advantages in the development of large-scale offshore wind power. This paper presents a motion study of a 5MW floating VAWT composed of the Φ type Darrieus wind turbine and the spar type floating foundation with heave plates. A computing code of aerodynamic loads was developed considering the dynamic stall and the floating foundation motions. The motion equations of the floating VAWT were established and solved numerically. Model tests were conducted, and the results of heave and pitch motion in test were compared with that of numerical calculation. The PRAOs (pseudo response amplitude operators) of numerical calculation are found to agree well with the experimental data with wave only conditions, and have some little discrepancies with wave and wind conditions. The surge-heave-pitch motions of the floating VAWT were analyzed. The results show that the aerodynamic forces have minimal influence on the heave motions of the floating VAWT, while they obviously increase the mean values of surge and pitch motions. The surge, heave and pitch frequencies of the floating VAWT are dominated by the wave frequencies, and the 2P (twice-per-revolution) response of pitch motions is not significant.

A Numerical Study of a Submerged Horizontal Heaving Plate as a Breakwater

ABSTRACT Liu, C.; Huang, Z., and Chen, W., 2017. A numerical study of a submerged horizontal heaving plate as a breakwater. Using a nonlinear numerical wave tank (NWT) based on potential flow, a submerged horizontal plate heaving in regular waves was simulated, and its performance as a breakwater was examined. The NWT is based on a Mixed Eulerian-Lagrangian formulation and a de-singularized boundary integral equation method. The viscous effect on the motion of the plate is estimated by a linear damping coefficient, and the natural frequency of the heaving plate is controlled by the system stiffness. Compared with a fixed submerged horizontal plate, our results showed that the heaving motion of the plate with a critical stiffness could reduce the wave-transmission coefficient to almost zero and effectively suppress the free and locked waves on the leeside of the plate. The new type of breakwater can be an ideal alternative for small marinas and recreational harbors.

A new type of anti-heave semi-submersible drilling platform

Abstract A new type of semi-submersible drilling platform is designed. The numerical simulation software is used to analyze the heave response of the new platform in the frequency domain and time domain, and the semi-submersible drilling platforms with double-floating four-column structure and heave plate structure are compared with the new platform. This paper introduces the design principles of the new platform and the theoretical basis, mathematical model and boundary conditions during correlation analysis. The numerical simulation results show that the maximum and mean values of the heave response of the new platform are significantly reduced in the frequency domain analysis compared with the double-floating four-column and the heave-plate structure platform; and the new platform has a significant increase in the natural heaving period of the new platform, which can effectively prevent the occurrence of resonance. In the mooring time domain coupling analysis, the surge, sway and roll response of the new platform is small, and the heave response is greatly reduced. In the spectral analysis, the new platform has a smaller peak response and better wave frequency characteristics. The new platform has excellent anti-heave performance, reasonable structure and feasibility, and can provide reference for the design and selection of new generation semi-submersible drilling platform.

Hydrodynamic characteristics of a separated heave plate mounted at a vertical circular cylinder

In this study, a wave flume experiment was performed with a scaled floating model to optimise the design of a floating body and control unwanted motions due to the offshore environment. A cylindrical test model was chosen as a standard and classical representative design of a floating structure in an ocean environment. The attachment of a heave plate at the bottom of the floating structure has been suggested as an effective tool to control its motion. However, the associated hydrodynamic effects, particularly the added mass variation, need to be investigated. Therefore, a scaled cylindrical model with a height of 300mm, an outer diameter of 60mm, and various heave plates was designed, manufactured, and tested. The motion responses of a scaled model in a water flume (i.e. forced oscillation, free decay, and regular wave response) were analysed. The results were compared for similar cylindrical models with various heave plates attached at different gaps from the cylinder bottom, different oscillating frequencies, and different Keulegan–Carpenter (KC) numbers. An empirical formula was formulated to calculate the added mass of the combined structure of the cylinder and heave plate. The results indicated that varying the heave plate diameter had the most significant effect on the added mass compared to the gap and KC (0.2–1.4). The added mass coefficient of the combined cylinder and heave plate was below 0.05, while KC varies from 0.2 to 1.4 and the gap ratio (Dg/(0.5Dc+0.5Dp)) varied between 0.2 and 1.2. The peak heave response amplitude operator (RAO) for the combined cylinder and heave plate was 40% less than that of the cylinder without a heave plate.

“Bigfoot” Direct Vertical Access Semisubmersible Model Tests and Comparison With Numerical Predictions

The Bigfoot direct vertical access (DVA) semisubmersible is a novel floating drilling and production host that provides an attractive alternative to the spar. This concept utilizes heave plates (big feet) that improve the motion characteristics of a semisubmersible in all mild environments (Southeast Asia, West Africa, and Brazil). Bigfoot offers riser-friendly motions that enable top-tensioned risers, which is often a project requirement. This floater works in all water depths, in particular ultra-deepwater (5000 + ft) where a tension leg platform (TLP) is not an option, supports top-tensioned risers, and enables drilling and workover operations. The Bigfoot has several advantages over a spar. These include: (1) quayside topsides integration. This eliminates offshore topsides integration, a significant issue for all spar projects in terms of cost, safety, and schedule, (2) a more open deck layout compared to a spar, and (3) no fabrication location restrictions as it can be built by many yards worldwide potentially offering local content to a project. Model tests were undertaken at the Shanghai Jiao Tong University (SJTU) Offshore Basin to assess the dynamic response of the Bigfoot in waves, swell, wind, and current. Five mild non-Gulf of Mexico (GOM) environments were considered. In all the cases, the floater motions are an order of magnitude smaller than those of a conventional semisubmersible for similar deck payload, thus enabling drilling operations and top-tensioned production risers. In a parallel effort, a cosmos numerical model of the Bigfoot was developed for coupled motion analysis. The experimental results and the cosmos numerical predictions are in close agreement. In addition to measuring global motions, two heave plates were instrumented with load cells to measure forces and moments. The force measurements from the model tests are in good agreement with numerical predictions using computational fluid dynamics (CFD).

Heave damping of spar platform for offshore wind turbine with heave plate

This paper presents the effects of heave plate on heave damping of spar with single and two heave plates for supporting the offshore wind turbine. Heave free decay tests are carried out experimentally on 1:50 scale model of spar with single and two heave plates for finding the heave damping. Heave dampings are also obtained numerically using Computational Fluid Dynamics (CFD) simulation and validated with the experimental results. Detailed parametric studies are conducted numerically on spar with single and two heave plates. Effects of scaling ratio (1–50), diameter ratio (1–2), heave plate position to diameter of heave plate ratio (0.2–1), heave plate position to draft ratio (0.2–0.8), relative spacing (0.2–1) and spacing between heave plates to draft ratio (0.2–0.8) are examined. Results show that the heave damping increases with increase in scaling ratio and diameter ratio. It is found that the diameter ratios of 1.2–1.4, position to diameter of heave plate ratio of 0.8, position to draft ratio of 0.4, relative spacings of 0.4–0.6 and spacing to draft ratios of 0.2–0.4 are more favorable conditions to reduce the heave motion.

A novel tuned heave plate system for heave motion suppression and energy harvesting on semi-submersible platforms

Deepwater offshore structures such as semi-submersible platforms suffer powerful ocean waves due to their location and site condition. The long distance away from the shore also brings many difficulties to energy supply for the platform operation. How to reduce the response of the platform and convert the wave energy into electrical power is a meaningful topic. In this paper, a tuned heave plate system (THP) is presented and designed to be employed on a semi-submersible platform for heave motion suppression and energy harvesting. This THP system is composed of spring supports, a power take-off system (PTO), and a heave plate. The PTO system is a permanent magnet linear generator (PMLG), which could directly convert the kinetic energy of the heave plate into electronic power. The stiffness of the spring supports is designed based on the principle of the tuned mass damper (TMD). The numerical model of the platform and the THP system is established according to the hydrodynamic analysis results of the platform. The model is tested and modified by scale model tests on the platform in the wave tank. A parameter study, including the size, tuned period, and damping ratio of the THP system, is conducted systematically based on the numerical model. The optimal parameters of the THP are selected due to the maximum heave motion reduction under severe wave conditions in South China Sea. The performance of the semi-submersible with and without the THP system under different wave conditions is analyzed. It is demonstrated that this novel tuned heave plate system could reduce the heave motion of the semi-submersible platform significantly and generate considerable power, which makes the THP system have a broad prospect for development.

Study of the force coefficients on plates using an open source numerical wave tank

An open source numerical wave tank based on the OpenFOAM® software was setup and tested to solve the Navier–Stokes equations. This work focused on submerged plates because of their simple geometry, their importance as a design component (e.g., heave plates), and the broad availability of published experimental results. Two-dimensional plates in an oscillatory flow, as well as three-dimensional circular disks and square plates undergoing forced oscillations were simulated in conditions where the nonlinearity of hydrodynamic viscous drag and inertia forces can be probed easily. The effect of plate thickness as well as the ability of the numerical simulations to predict wave radiation damping at shallow plate submergence were also considered. Overall, force coefficient predictions were very satisfactory when compared to experimental data, and generally exhibited less scatter. The influence of both Keulegan–Carpenter number and frequency parameter on the hydrodynamic force could be assessed as well from these numerical simulations as from past laboratory experiments.

Experimental Study on the Suppression of a Vertical Circular Cylinder with a Heave Plate

Studies of floating structures are becoming increasingly important due to their increased application. The hydrodynamic motion response of floating structures must be controlled within a certain range, especially in the resonance region. In this study, a scale model of a circular cylinder having a height of 300 mm, outer diameter 60 mm, natural heave period 0.78 s and a natural pitch period 1.12 s, was designed and analyzed for hydrodynamic load. We compared this model with other models of cylinders with various heave plates systems. In order to find the size effect of the heave plate, two heave plates of 60 and 80 mm in diameter with a thickness of 5 mm. At first, a free decay experiment was carried out to examine the damped heave and pitch period, as well as the hydrodynamic coefficients in the resonance frequency. The motion response was also analyzed to obtain the heave and pitch motion response in a series of regular waves having periods between 0.51 s and 1.24 s. It was observed that the heave plate significantly enhanced the damped heave period, whereas it had a negligible effect on the damped pitch period. Moreover, the peak of heave Response Amplitude Operator (RAO) was observed to be reduced for the heave plate in the resonance region and the peak of heave RAO was shifted to a long period. Furthermore, a comparatively small peak heave RAO was observed in the experiments. It was indicated that pitch motion has an effect on heave motion in the pitch resonance frequency.

Numerical Investigation of a Tuned Heave Plate Energy-Harvesting System of a Semi-Submersible Platform

A novel tuned heave plate energy-harvesting system (THPEH) is presented for the motion suppressing and energy harvesting of a semi-submersible platform. This THPEH system is designed based on the principle of a tuned mass damper (TMD) and is composed of spring supports, a power take-off system (PTO) and four movable heave plates. The permanent magnet linear generators (PMLG) are used as the PTO system in this design. A semi-submersible platform operating in the South China Sea is selected as the research subject for investigating the effects of the THPEH system on motion reduction and harvesting energy through numerical simulations. The numerical model of the platform and the THPEH system, which was established based on hydrodynamic analysis, is modified and validated by the results of the flume test of a 1:70 scale model. The effects of the parameters, including the size, the frequency ratio and the damping ratio of the THPEH system, are systematically investigated. The results show that this THPEH system, with proper parameters, could significantly reduce the motions of the semi-submersible platform and generate considerable power under different wave conditions.

Experiment study of dynamics response for wind turbine system of floating foundation

The floating foundation is designed to support a 1.5 MW wind turbine in 30 m water depth. With consideration of the viscous damping of foundation and heave plates, the amplitude-frequency response characteristics of the foundation are studied. By taking into account the elastic effect of blades and tower, the classic quasi-steady blade-element/momentum (BEM) theory is used to calculate the aerodynamic elastic loads. A coupled dynamic model of the turbine-foundationmooring lines is established to calculate the motion response of floating foundation under Kaimal wind spectrum and regular wave by using the FAST codes. The model experiment is carried out to test damping characteristics and natural motion behaviors of the wind turbine system. The dynamics response is tested by considering only waves and the joint action of wind and waves. It is shown that the wind turbine system can avoid resonances under the action of wind and waves. In addition, the heave motion of the floating foundation is induced by waves and the surge motion is induced by wind. The action of wind and waves is of significance for pitch.

Computation of flow features and hydrodynamic coefficients around heave plates oscillating near a seabed

For the past few years, heave plates have been used in the offshore industry due to their favorable hydrodynamic characteristics in oscillating flows, i.e., increased added mass and damping. The hydrodynamic coefficients of heave plates are strongly influenced by the proximity of solid boundaries. Assessing how this variation depends on the proximity to the seabed and on the amplitude of the oscillation is the main aim of this paper. In this process, a new model describing the work done by damping in terms of the flow enstrophy is described herein. This new approach is able to provide a direct correlation between the vortex shedding processes and the linear damping coefficient. Numerical simulations have been performed using the finite volume open source solver OpenFOAM. Simulations have been conducted on a solid circular disc oscillating axially in water at various elevations above an impermeable seabed boundary. Results for hydrodynamic coefficients are validated against previously published experimental data. At low KC numbers, a systematic increase in added mass and damping, corresponding to an increase in the seabed proximity, is observed. As seen in experiments, a critical KC where the monotonic trend of the hydrodynamic coefficients with KC is disrupted and that depends on the seabed distance exists. The physical behavior of the flow around the critical KC is explained through an analysis of the flow enstrophy.

Manufacturing and design of the offshore structure Froude scale model related to basin restrictions

Manufacturing steps for a modern three - column semi-submersible structure are delivered using CFD/CAE software and actual Froude scaled model testing. The three- column offshore is part of the Wind Float Project already realized as prototype for wind energy extraction in water depths more than 40 meters, and the actual model will not consider the wind turbine. The model will have heave plates for a smaller heave motion in order to compare it with the case without heave plates. The heave plates will be part of the Froude scale model.. Using a smaller model will determine a smaller heave motion and this will affect predictions of the vertical movement of the three- column offshore structure in real sea. The Froude criterion is used for the time, speed and acceleration scale. The scale model is manufactured from steel and fiberglass and all parts are subjected to software analysis in order to get the smallest stress in connections inside the model. The model mass was restricted by scale dimensions and also the vertical position of centre gravity will be considered during the manufacturing and design process of the Froude scale offshore structure. All conditions must converge in model manufacturing and design in order to get the best results to compare with real sea states and heave motion data.

Hydrodynamic coefficients and pressure loads on heave plates for semi-submersible floating offshore wind turbines: A comparative analysis using large scale models

Hydrodynamic forces on heave plates for a semi-submersible floating offshore wind turbine are discussed herein. A model of one of the platform columns has been built. This allows for the fitting of either a plain solid plate or the real heave plate prototype design. The latter is equipped with a vertical flap at its edge. The influence of the flap on the hydrodynamic coefficients is investigated through a results comparison with the plain solid one. The model plate diameter is 1 m, thus becoming, to the authors' knowledge, the largest for which results have been published. Results from experiments, in which added mass and damping coefficients have been measured, are presented. This experimental campaign also comprised the direct measurement of dynamic pressures on both heave plates, a fundamental magnitude for the structural design, which, until now, had not been experimentally explored for this type of system. For comparative reasons, numerical simulations were also conducted following common industry standards, both with a wide-spread frequency domain panel method (WADAM) and a RANS CFD commercial code (ANSYS CFX). Finally, results are compared with literature and consistent non-dimensionalizations are sought, with the aim of making these results useful for preliminary design purposes. The authors believe this research could benefit the offshore wind industry by improving the hydrodynamic design of the concept.

Effect of Viscous Damping on Hydrodynamic Response of Spar with Heave Plate

In the present paper, effect of viscous damping on the heave response of spar is studied using WAMIT software for spar with single and two heave plates. For spar with single heave plate, a plate is attached at the keel of the spar and the diameter of the heave plate is varied. Diameter ratio (i.e., ratio of diameter of heave plate to diameter of spar – Dp/Ds) of 1.1 to 1.4 is considered here. For spar with two heave plates, one plate is fixed at the keel of the spar and other plate is placed at some distance from the keel. Diameter of the two plates is same and diameter ratio of 1.3 is taken for these plates. Spacing between the plates is varied and relative spacing (i.e., ratio of spacing between the two heave plates to diameter of heave plate - L/Dp) of 0.1 to 0.4 is considered. WAMIT software is based on potential theory so it considers only radiation damping. To account the viscous damping in WAMIT analysis, viscous damping values obtained from the literatures are used as an external damping matrix in WAMIT software. Increase in diameter ratio and relative spacing increases the heave added mass and damping of the spar. Hence, heave response of spar reduces with increase in diameter of the heave plate and spacing between the two heave plates. It is found that heave viscous damping reduces the heave response of spar with heave plate significantly. It is suggested that viscous damping should be included in WAMIT software for the reduction of heave response of spar with heave plate. Diameter ratio of 1.2 to 1.3 and relative spacing of 0.2 to 0.3 are recommended for significant heave motion reduction.